Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equations

The present paper is concerned with the numerical solution to initial value problems of neutral delay integro-differential equations (NDIDEs). The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for a class R(α,β1,β2,γ) of nonlinear systems of NDIDEs are derived. A numerical test that confirms the theoretical results is given in the end.